Jorge Martínez — known by his nickname "Aspar" — established the team in 1992 while still an active rider himself, initially operating a Honda RS125R in the 125 cc class. In 1993 he expanded operations into the 250 cc class, debuting with rider Juan Borja. Over the following two seasons the team ran Yamaha TZ125 machinery before commencing an eighteen-year partnership with Aprilia in 1996.
During the Aprilia years the team built a reputation as a nursery for talent, fielding riders including Fonsi Nieto and Arnaud Vincent. The team returned to the 250 cc class in 2000 with Alex Debón, and through the 2000s cycled a number of significant names through its 250 cc entry including Toni Elías, Alex de Angelis, Sebastián Porto, and Randy de Puniet.
The team's most concentrated period of success came in the 125 cc World Championship between 2006 and 2011, when Aspar riders won four world titles: Álvaro Bautista in 2006, Gábor Talmácsi in 2007, Julián Simón in 2009, and Nicolás Terol in 2011. During the same period, Terol finished second in 2010 while teammate Bradley Smith placed fourth, illustrating the team's consistent front-running capability.
In 2010, Aspar entered the MotoGP class for the first time, fielding Héctor Barberá on a Ducati Desmosedici GP10, with Barberá finishing twelfth overall. Simultaneously, the team entered the inaugural Moto2 season with Julián Simón and Mike Di Meglio, both starting on Honda-powered RSV Motors frames before switching to a Suter chassis after two races. Simón finished second in the inaugural Moto2 standings.
Barberá continued with the MotoGP programme in 2011, recording a best result of sixth at the Spanish Grand Prix. From 2012 the team ran in the Claiming Rule Teams (CRT) category with an ART machine, with Aleix Espargaró and Randy de Puniet dominating that classification for two consecutive years. In 2014, the team signed former World Champion Nicky Hayden alongside Hiroshi Aoyama on Honda machinery.
Before the 2018 season the team renamed itself Ángel Nieto Team as a tribute from team principal Jorge Fernandez to the late Spanish motorcycling legend Ángel Nieto. Gelete Nieto, Ángel's son, became the new team principal. The team reverted to the Aspar name at the start of the 2020 season.
Aspar secured their first world championship since 2011 when Albert Arenas won the Moto3 title in 2020. Further Moto3 titles followed with Izan Guevara in 2022 and David Alonso in 2024. Alonso's 2024 campaign was historic: he set records for the most Moto3 wins overall, most consecutive Moto3 victories, and most wins in a single season across all Grand Prix classes.
In 2024 the team began a technical and commercial partnership with Chinese manufacturer CFMoto, subsequently extended to 2031, signalling a long-term strategic commitment to the team's future in the world championship.